Rubber isolators are important connecting and vibration-damping components in the auxiliary systems of aero-engines. Their vibration isolation performance is susceptible to material aging and uncertainties in service environments， making reliability assessment an urgent need. However， the traditional Monte Carlo method， which relies on a large number of random samples， incurs high computational costs. For typical aviation components like isolators-characterized by complex structures， multiple uncertain factors， and high test costs-existing methods still struggle to achieve reliability assessment with both computational efficiency and statistical accuracy. To address this issue， The study proposes an uncertainty quantification method based on moment quadrature and maximum entropy theory， enabling efficient reliability assessment of the vibration isolation performance of rubber isolators. First， an elastic modulus degradation model is established based on the accelerated aging test data of rubber materials. Optimal integration nodes and weights are derived by constructing a Hankel matrix through moment quadrature， replacing large-scale random sampling with a small number of key samples. Subsequently， the elastic moduli corresponding to the integration nodes are input into the random vibration finite element model to obtain the vibration isolation rate response and its statistical moments. The maximum entropy principle is then used to reconstruct the probability density function of the vibration isolation rate without the need to preset a distribution form. This method features significant advantages of being non-sampling and analytical quadrature. It can obtain multi-order statistical characteristics of vibration isolation performance with only a few optimal integration nodes， greatly reducing the number of finite element calls while maintaining accuracy. It provides an efficient technical approach for reliability analysis of complex structures.